JP2005283502A - Method for analyzing sample - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To enable a sample which has a dielectric film whose dielectric constant is not less than 50 on the basis of an electrical measurement, to be analyzed over the entire optical range, based on a measurement result of an ellipsometer. <P>SOLUTION: The sample, wherein on a substrate the dielectric film is formed, whose dielectric constant is not less than 50 on the basis of the electrical measurement, is measured by the ellipsometer, and a model according to the sample is created, based on an effective medium approximation (EMA). In the model, a film corresponding to the dielectric film is formed so as to have the void ratio in the range of 60% to 90%. A value, calculated from the model, is compared to a value measured by the ellipsometer, and a fitting process is carried out so that the difference between both values becomes small, thereby specifying the film thickness and the optical constants of the sample. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  In the present invention, when a sample having a dielectric film formed of a ferroelectric material or a high-dielectric material is analyzed using an ellipsometer, a model including a large amount of voids based on the effective medium approximation is created to cover the entire optical range. The present invention relates to a sample analysis method capable of analyzing a sample.

  Conventionally, an ellipsometer is sometimes used to analyze information about a sample. The ellipsometer obtains a phase difference (Δ delta) and an amplitude ratio (Ψ psi) by making light in a polarized state incident on a sample and measuring changes in the polarization state of incident light and reflected light. Samples to be analyzed include those with a single substrate and those with a film formed on the substrate.

  FIG. 9 is a graph showing the results of measuring a sample having a silicon oxide film formed on a silicon substrate with an ellipsometer. The horizontal axis represents the wavelength of light incident on the sample (nm nanometer), the right vertical axis represents the measured phase difference (Δdelta), and the left vertical axis represents the measured amplitude ratio (Ψ psi). In addition, when the wavelength of the incident light is 633 nm, the complex dielectric constant (static dielectric constant) based on the optical measurement of the silicon oxide film is about 2.1.

  In addition, from the phase difference and amplitude ratio obtained by the above-described ellipsometer measurement, the refractive index (n), extinction coefficient (k), and film thickness (d) of the film can be directly obtained with only one set for the sample. I can't. Therefore, in order to obtain the refractive index, extinction coefficient, and film thickness of the film with only one set, in addition to the measurement by the ellipsometer, a model corresponding to the sample is created, and the phase difference theoretically obtained from this model is obtained. Then, the amplitude ratio is compared with the phase difference and amplitude ratio obtained by the ellipsometer measurement. The model is created by setting the conditions according to the physical properties of the sample. The conditions to be set include the substrate and film material, the film thickness of each film layer, and the optical constants of the substrate and film. There is. For setting each item, a known reference corresponding to the sample, a required dispersion formula showing the wavelength dependence of the dielectric constant and having a plurality of parameters, and the like are usually used.

  Further, for the above comparison, a process of changing the parameters of the dispersion formula and the thickness of each film layer of the model so as to minimize the difference between the two (referred to as fitting) is performed. The difference between the two is usually obtained by calculation using the least square method, and if it is determined that the result obtained by the least square method has been reduced to some extent by fitting, the value of the parameter of the dispersion equation at that time The refractive index and extinction coefficient are determined, and the film thickness at that time is specified as the film thickness of the film of the sample. In general, model creation, least squares calculation, fitting, and the like are performed manually or automatically based on a required program using a computer (see Patent Documents 1 and 2).

  In the analysis method described above, as shown in FIG. 10A, the boundary between the substrate S1 and the film S2 constituting the sample S is a flat surface, the film S2 is a parallel film, and the material constituting the film S2 is homogeneous and continuous. If it is, it can be done without any problems. However, as shown in FIG. 10B, since the actual sample S has irregularities (roughness) on the surface of the film S2, good results can be obtained even if the above-described analysis method is performed as it is depending on the degree of roughness. May not be obtained.

  Therefore, in such a case, using the concept of effective medium approximation, the film S2 having the roughness shown in FIG. 10B is made uniform and continuous as shown in FIG. 10C. In the first film S2a whose film thickness is d1 and the substance M related to the film S2, voids V are present at a required rate (void ratio, hereinafter referred to as void), and the film thickness is d2. A model replaced with the second film S2b is formed. According to the model thus formed, the film thickness d1 of the first film S2a, the film thickness d2 of the second film S2b, the mixing ratio (void fraction) of the substance M and the voids in the second film S2b, and the sample The sample is analyzed by fitting the parameters of the dispersion formula.

  The number of voids set for the model is determined based on the roughness, but the maximum value for voids is generally considered to be about 40-55% considering the range where the film can be formed. Usually, a numerical value of 50% is often used. If it is unclear whether roughness exists on the film surface of the sample, both the analysis method using the effective medium approximation described above and the analysis method not using the effective medium approximation are performed. It is common to determine whether or not there is roughness by determining whether the actual sample is more compatible by using the least squares calculation result or the like.

  The effective medium approximation may be applied not only to the case where roughness exists on the film surface of the sample, but also to the interface layer where roughness exists at the interface between the substrate and the film or between the film layers. . Further, the effective medium approximation is used to lower the refractive index as a technique for actually performing the analysis regardless of the presence of roughness. Also in this case, whether or not to use the effective medium approximation is determined based on an analysis result of a model having a gap based on the effective medium approximation and whether or not the effective medium approximation is used.

For example, consider the case of analyzing a sample in which a first film of amorphous silicon is formed on a glass substrate and a second film of a natural oxide film is formed on the first film. For this sample, first, the first film thickness is set to 2000 angstroms, the second film thickness is set to 20 angstroms, and a model is created using a known amorphous silicon reference. , It is assumed that the calculation result of the least square method (corresponding to the mean square error χ ² ) is 16.6.

  Next, the film thicknesses of the first film and the second film are made the same as described above, and the amorphous silicon occupancy of the first film is 50% and the void of the first film is 50% using the effective medium approximation regardless of the roughness. When a model is created using a known amorphous silicon reference and fitting is performed in the same manner as described above, the calculation result of the least square method is 10.6, and the amorphous silicon occupied in the first film Assume that the rate is about 86%. Since the calculation result of the least squares method is better when the numerical value is smaller, analysis is performed compared to the first case by creating a model using a known reference and providing a void based on the effective medium approximation. It turns out that a result (fitting result) became favorable.

Finally, the film thicknesses of the first film and the second film are made the same as in the first case, the effective medium approximation is used regardless of the roughness, and the amorphous silicon occupancy in the second case is taken into consideration. Assume that the silicon occupation rate is set to 86%, the void of the first film is set to 14%, a model is created using a dispersion formula instead of a reference, and fitting is performed in the same manner as described above. As a result, if the calculation result of the least square method is 0.14 and the occupation ratio of the amorphous silicon of the first film is about 99.16%, the calculation result of the least square method becomes very good. However, since the void is close to 0%, it can be seen that it has become meaningless to create a model with voids. Therefore, in such a case, generally, a model that does not form voids is created using a dispersion formula and analyzed.
JP 2002-340789 A JP 2002-340528 A

  In an analysis method based on optical measurement using a conventional ellipsometer, when a sample has a high dielectric film or a ferroelectric film having a dielectric constant of 50 or more based on electrical measurement, a required optical range is obtained. Therefore, there is a problem that the physical properties of the sample cannot be analyzed based on the complex dielectric constant.

  That is, in the analysis method using the conventional ellipsometer, the total optical range relating to the wavelength of light (DUV (Deep Ultraviolet) to NIR (Near Infrared): 190 nm to 1700 nm, the photon energy range corresponds to 0.75 eV to 6.5 eV). 248 nm to 826 nm in general) is the analysis range. High dielectrics and ferroelectrics have three parts as electronic polarizabilities: electronic polarizability, ionic polarizability, and dipole polarizability. It has been found that in the optical range of 400 nm or less, the refractive index and extinction coefficient are optically measured for high dielectrics and ferroelectrics, and a measurement result having a sharp peak is obtained. However, it is generally considered that a dispersion formula and a reference that can correspond to such a measurement result have not been found at present. For this reason, high dielectrics and ferroelectrics cannot be analyzed in the optical range of 400 nm or less (248 nm to 400 nm), and how the refractive index and extinction coefficient of the high dielectrics and ferroelectrics are in the optical range of 400 nm or less. The actual situation is that there are no books, documents, etc. that accurately describe whether or not it changes. The electrical measurement is for measuring the dielectric constant in the frequency range of 100 kHz to 1 MHz outside the near-infrared range included in the optical measurement range, and the measurement range of both the electrical measurement and the optical measurement. Are completely different.

  In addition, since the dielectric constant of the sample varies depending on the measurement range, the above-described problem occurs at 400 nm or less in the optical measurement range. Therefore, it is necessary to analyze the physical properties of a high dielectric material or a ferroelectric material in an optical measurement range of 400 nm or less using another device that is expensive and requires analysis time.

  In view of such a problem, the present invention was made as a result of the inventor's earnest research on the analysis of high dielectrics and ferroelectrics, and effective medium approximation was performed regardless of the presence of roughness. Providing a sample analysis method that enables analysis of high dielectrics or ferroelectrics even in the optical measurement range of 400 nm or less by creating the model used and setting the value of the void to a value exceeding the normal range. The purpose is to do.

  In order to solve the above-described problems, a sample analysis method according to the first invention is an ellipsometer that applies polarized light to a sample in which a dielectric film having a dielectric constant of 50 or more based on electrical measurement is formed on a substrate. An incident step, a step of measuring a change value of a polarization state of incident light and reflected light with respect to the sample, and a condition corresponding to the sample are set, and a gap based on an effective medium approximation is 60% or more and 90% or less A step of creating a model existing in a range; a step of calculating a value corresponding to a change value of a polarization state measured by the ellipsometer based on the created model; and a calculated value and a change value measured by the ellipsometer. A step of comparing, a step of performing an operation according to an arithmetic expression related to the effective medium approximation and a dispersion expression related to the model so that a difference between the compared two values is small; Characterized in that it comprises the steps of analyzing a sample based on the result of the operation.

  In the first invention, a sample having a high dielectric film or a ferroelectric film having a dielectric constant of 50 or more based on electrical measurement is measured with an ellipsometer, and the voids are dielectric films based on the effective medium approximation. A model that exists at 60% or more and 90% or less in the film corresponding to the above is created and the sample is analyzed. Such a void of 60% or more and 90% or less is a value that is not normally set because it is difficult to form a film based on a physical viewpoint. However, it is possible to mathematically fit a sample having a high dielectric film or a ferroelectric film that can correspond to a measurement result having a sharp peak by setting a numerical value in the above-mentioned range. Thus, the sample can be analyzed even in an optical measurement range of 400 nm or less, which has been impossible in the past from the result of fitting.

  According to the inventor's research, it has been found that if the void is set in a range of 65% or more and 75% or less, the difference obtained by the least squares method is likely to be small. In particular, it is determined that it is preferable to set the air gap in the range of 67% or more and 73% or less, which is around 70%, because the fitting can be performed efficiently.

  In the sample analysis method according to the second invention, the dispersion formula includes a parameter related to a dielectric constant with respect to an optical measurement range, and an optical measurement range of a dielectric film of the sample based on a numerical value of the parameter related to the dielectric constant The dielectric constant is analyzed.

  In the second aspect of the invention, an optical film having a dielectric constant of 50 nm or more based on electrical measurement with a dielectric constant of 50 nm or less is referred to a value set for a parameter relating to a dielectric constant of the dispersion formula. The dielectric constant in a specific measurement range. As a result, it is no longer necessary to analyze the physical properties using other expensive and time-consuming apparatuses as in the past, and the conventional analysis of physical properties for high dielectrics or ferroelectrics based on the specified dielectric constant. Compared to this, it can be performed quickly and easily.

In the first invention, a model is created in which a void exists between 60% and 90% based on the effective medium approximation for a sample having a dielectric film having a dielectric constant of 50 or more based on electrical measurement. In addition, by performing fitting on the value measured by the ellipsometer, the sample can be analyzed even in an optical measurement range of 400 nm or less, which has been impossible in the past.
In the second invention, the physical property can be analyzed by obtaining the dielectric constant within the optical measurement range of 400 nm or less for a sample having a dielectric film having a dielectric constant of 50 or more based on electrical measurement. In addition, the cost, time, labor and the like related to the physical property analysis of the sample based on the dielectric constant can be greatly reduced as compared with the conventional case.

  FIG. 1 is a schematic diagram showing the overall configuration of an ellipsometer 1 and a computer 10 used in a sample analysis method according to an embodiment of the present invention. As shown in FIG. 2 (a), the ellipsometer 1 makes light in a polarized state incident on a sample S having a film S2 formed on a substrate S1, and changes each light according to a change in the polarization state of incident light and the polarization state of reflected light. The phase difference Δ and the amplitude ratio Ψ are measured. In the present invention, a sample S on which a ferroelectric or high-dielectric film S2 having a dielectric constant of 50 or more based on electrical measurement is formed is analyzed, and the structure other than the structure shown in FIG. A sample in which a plurality of films are formed on the substrate S1 and at least one of these films is the ferroelectric substance or the high dielectric substance is also an object of analysis.

  Further, the computer 10 creates a model corresponding to the sample using a dispersion formula and a reference, obtains a phase difference and an amplitude ratio from the model, and compares the phase difference and the amplitude ratio measured by the ellipsometer 1 with each other. Fitting is performed to analyze the refractive index, extinction coefficient, and complex dielectric constant as the film thickness and optical constant of the film. The computer 10 of the present embodiment uses an effective medium approximation (EMA) to create a model, creates a model in which voids are provided in a dielectric film in a range of 60% to 90%, and performs fitting. Do.

  First, the structure of the ellipsometer 1 shown in FIG. 1 as an example of an ellipsometer usable in the present invention will be described. The ellipsometer 1 connects a xenon lamp 2 and a light irradiator 3 with a first optical fiber cable 15a, and makes polarized light incident on the sample S placed on the stage 4 and also reflects the light reflected by the sample S. The light acquisition unit 5 captures the light. The light acquisition unit 5 is connected to the spectroscope 7 via the second optical fiber cable 15b, and the spectroscope 7 measures the polarization state of the light captured by the light acquisition unit 5. The spectroscope 7 transmits the measured polarization state as an analog signal to the data acquisition device 8, converts the analog signal into a required value by the data acquisition device 8, and transmits the measurement value of the ellipsometer 1 to the computer 10.

  The stage 4, the light irradiator 3, the light acquirer 5, and the spectrometer 7 are provided with a first motor M <b> 1 to a sixth motor M <b> 6, respectively, and the driving of each motor M <b> 1 to M <b> 6 is connected to the computer 10. The motor controller 9 is controlled. The motor controller 9 controls each of the motors M1 to M6 based on an instruction output from the CPU 11a of the computer 10.

The xenon lamp 2 of the ellipsometer 1 is a white light source including a large number of wavelength components, and sends the generated white light to the light irradiator 3.
The light irradiator 3 is disposed on the arc-shaped rail 6 and has a polarizer 3 a inside. The white light is polarized by the polarizer 3 a and is incident on the sample S. Further, the light irradiator 3 moves along the rail 6 when the fourth motor M4 is driven, and the angle of the incident light with respect to the perpendicular H of the surface Sa of the sample S (incident angle φ) is adjusted.

  The stage 4 is in the X, Y direction (see FIG. 1) and the height direction, which are directions different by 90 degrees on the placement surface 4a on which the sample S is placed by driving the first motor M1 to the third motor M3. Each can be moved in the Z direction. By moving the stage 4 in this way, light is made incident on a required portion of the sample S so that a plurality of portions of the sample S can be measured.

  Similar to the light irradiator 3, the light acquirer 5 is disposed on the rail 6, and includes a PEM (Photo Elastic Modulator) 5a and an analyzer 5b, and the light reflected by the sample S is converted into the PEM 5a. To the analyzer 5b. The light acquisition unit 5 can be moved along the rail 6 by the fifth motor M5 so that the light reflected by the sample S can be reliably captured. The movement of the light acquisition device 5 is controlled by the motor controller 9 so as to be interlocked with the movement of the light irradiation device 3, and the reflection angle φ and the incident angle φ are the same angle. The PEM 5a incorporated in the light acquisition unit 5 obtains elliptically polarized light from linearly polarized light by phase-modulating the captured light at a required frequency (for example, 50 kHz). By obtaining such polarized light, the measurement speed and The measurement accuracy is improved. The analyzer 5b transmits a specific polarized light from among various polarized lights phase-modulated by the PEM 5a.

  As shown in FIG. 3, the spectroscope 7 includes a reflection mirror 7a, a diffraction grating 7b, a photomultiplier (PMT: photomultiplier tube) 7c, and a control unit 7d, and a second optical fiber cable 15b from the light acquisition unit 5. The light transmitted through is reflected by the reflection mirror 7a and guided to the diffraction grating 7b. The angle of the diffraction grating 7b can be changed by the sixth motor M6 shown in FIG. 1, and since the diffraction direction of the light guided by the angle change changes, the wavelength of the light emitted from the diffraction grating 7b can be changed. I have to. Although not shown in FIG. 3, a sine bar mechanism that performs dial display by mechanically converting the angle of the diffraction grating 7b so that the wavelength corresponding to the changed angle of the diffraction grating 7b can be numerically indicated. Are linked. The spectroscope 7 can also be used in combination with a photomultiplier 7c and a photodiode array (PDA).

  The light emitted from the diffraction grating 7b is measured by the PMT 7c, and the control unit 7d generates an analog signal corresponding to the measured wavelength and sends it to the data acquisition unit 8. In this way, the spectroscope 7 measures each wavelength by changing the angle of the diffraction grating 7b, so that the measurement accuracy is good. As a result, the spectroscope 7 can measure by changing the wavelength according to the film thickness of the film layer of the sample. For example, when the film thickness is thick, the wavelength can be changed in fine steps. The spectroscope 7 may have a configuration in which a plurality (32 or 64, etc.) of photomultipliers corresponding to different wavelengths are arranged in a fan shape with respect to the diffraction grating.

The data acquisition device 8 calculates the phase difference Δ and the amplitude ratio Ψ of the polarization state (p-polarized light, s-polarized light) of the reflected light measured based on the signal from the spectroscope 7, and sends the calculated result to the computer 10. To do. The phase difference Δ and the amplitude ratio Ψ satisfy the following relationship (1) with respect to the amplitude reflection coefficient Rp of p-polarized light and the amplitude reflection coefficient Rs of s-polarized light.
Rp / Rs = tan Ψ · exp (i · Δ) (1)
However, i is an imaginary unit (the same applies hereinafter). Rp / Rs is called the polarization change amount ρ.

  On the other hand, the computer 10 includes a computer main body 11, a display 12, a keyboard 13, a mouse 14, and the like. The computer main body 11 is internally connected to a CPU 11a, a storage unit 11b, a RAM 11c, a ROM 11d, and the like via an internal bus. The CPU 11a performs various processes to be described later according to various computer programs stored in the storage unit 11b. The RAM 11c temporarily stores various data related to the processing, and the ROM 11d stores the contents related to the function of the computer 10 and the like. In addition to various computer programs, the storage unit 11b stores known data related to the manufacturing process of the sample S, a plurality of dispersion formulas used for creating models, reference data corresponding to various samples, and the like. Yes.

  When the complex refractive index of the periphery of the sample S and the substrate S1 is known from the phase difference Δ and the amplitude ratio Ψ transmitted from the data fetcher 8, the computer 10 performs modeling stored in advance in the storage unit 11b. By using the program, a model corresponding to the material structure of the sample S shown in FIG. 2A is created to determine the film thickness d of the film S2 and the complex refractive index N of the film S2. In this embodiment, for model creation, the effective medium approximation is used regardless of the presence or absence of the roughness of the sample S, and the dielectric constant based on electrical measurement is 50 on the substrate S1 ′ as shown in FIG. A model S ′ having a structure in which a film S2 ′ in which a void V (air component) is present in the dielectric substance M (dielectric component) is formed.

When the complex refractive index N is the refractive index n and the extinction coefficient k of the film, the relationship expressed by the following optical formula (2) is established.
N = n−ik (2)
Further, if the wavelength of the light irradiated by the light irradiator 3 of the ellipsometer 1 is λ, the phase difference Δ and the amplitude ratio Ψ calculated by the data acquisition device 8 are the film thickness d and the refractive index related to the film of the sample S. The relationship of n and the extinction coefficient k and the following formula (3) is established.
(D, n, k) = F (ρ) = F (Ψ (λ, φ), Δ (λ, φ)) (3)

Further, the computer 10 uses a model spectrum (Ψ _M) theoretically obtained from the created model by using the film thickness of the film of the sample S and the dispersion formula indicating the wavelength dependence of the complex dielectric constant having a plurality of parameters. (Λ _i ), Δ _M (λ _i )) and the measurement spectrum (Ψ _E (λ _i ), Δ _E (λ _i )) related to the measurement result of the ellipsometer 1 A process (fitting) for changing the parameters of the dispersion formula is performed. As a result of the fitting, the value related to the model is changed and determined, and the changed value includes the set mixing ratio of the voids. In the present embodiment, the following formula (4) is applied as a dispersion formula.

In Equation (4), ε on the left side represents a complex dielectric constant, ε _∞ and ε _s represent dielectric constants, Γ ₀ , Γ _D , and γ _j represent damping factors with respect to viscous force, ω _oj , ω _t and ω _p represent natural angular frequencies (oscillator frequency, transverse frequency, plasma frequency). Note that ε _∞ is a dielectric constant at a high frequency (high frequency dielectric constant), and ε _s is a dielectric constant at a low frequency (static dielectric constant).

In the case of this embodiment, the void of the model void V is set in the range of 60% to 90%, and the parameters of ε _s , ω _t , and Γ ₀ in the second term are fitted by the dispersion formula of Formula (4). Then, using known values for the other parameters, the calculation is performed with ε _{∞ of} the first term set to “1” and the third and fourth terms set to “0”. As a result of the fitting, the film thickness and the like are obtained, and the complex dielectric constant ε of the material can be obtained from Equation (4) from the parameters of the dispersion equation. The complex dielectric constant ε (corresponding to ε (λ)) and the complex refractive index N (corresponding to N (λ)) satisfy the relationship of the following formula (5).
ε (λ) = N ² (λ) (5)

The contents of the fitting will be described. When the sample S is measured by the ellipsometer 1, T measurement data pairs are represented as Exp (i = 1, 2,..., T), and T model calculation data pairs are represented as When Mod (i = 1, 2,..., T), the measurement error is normally distributed, and the mean square error χ ² according to the least square method when the standard deviation is σ _i is expressed by the following equation (6). ). P is the number of parameters. When the value of the mean square error χ ² is small, it means that the degree of coincidence between the measurement result and the formed model is large, so when comparing multiple models, the one with the smallest mean square error χ ² value Corresponds to the best model.

  A series of processes performed by the computer 10 described above is defined in a computer program stored in the storage unit 11b, and in this computer program, as shown in FIG. Processing for displaying a menu 20 to be set by inputting a film thickness, a void or the like, which is a condition item, is also programmed. In the present embodiment, when a void is set for the film S2 ′ in FIG. 2B, the ratio of the substance M forming the film S2 ′ can be automatically set, and the ratio of the substance M in the film S2 ′ is set. Then, the void of the film S2 ′ is automatically set. Therefore, it is only necessary to set a numerical value of either the void or the substance M constituting the film for the film S2 ′. For example, if the substance M of the film S2 ′ is set to 30%, the void of the film S2 ′ is automatically set to 70%.

Next, a series of procedures of the sample analysis method of the present invention using the ellipsometer 1 and the computer 10 having the above-described configuration will be described based on the flowchart of FIG.
First, a sample S in which a dielectric film having a dielectric constant of 50 or more is formed on the substrate is placed on the stage 4 of the ellipsometer 1 (S1). Next, the measurement location of the sample S, the incident angle φ, conditions for creating a model corresponding to the sample (substrate material, dielectric film thickness, optical constant, etc.), etc. are input to the computer 10 as items related to the analysis. (S2). In the present invention, the numerical value of the void is also input to the above condition, and in the present invention, a numerical value in the range of 60% to 90% (for example, 70%) is input. In addition, by inputting the conditions in this way, a model (see FIG. 2B) is formed in which a dielectric film is formed in which a gap based on the effective medium approximation is present at the input numerical mixture ratio (see FIG. 2B). S3).

Then, the ellipsometer 1 moves the light irradiator 3 and the light acquirer 5 and moves the stage 4 so that the incident angle φ and the reflection angle φ become the input numerical values, and the polarized light is incident on the sample. Then, the phase difference Δ _E and the amplitude ratio Ψ _E are measured (S5). Further, the computer 10 calculates the phase difference Δ _M and the amplitude ratio Ψ _M from the created model (S6), and compares the measured value of the ellipsometer 1 with the calculated value obtained from the model (S7). Fitting of the void mixing ratio, the dielectric mixing ratio, the film thickness, and the dispersion formula parameters in the model dielectric film is performed so that the difference between the compared values becomes small (S8).

  If the difference obtained by the least square method by fitting falls within the required value (if it is sufficiently small), the film thickness, optical constant, etc. of the sample from the film thickness, dispersion parameters, voids, numerical values of the mixing ratio, etc. Is obtained (S9). Thus, this invention analyzes the sample by calculating | requiring a film thickness and an optical constant. Each parameter in the dispersion formula relates to a dielectric component in the dielectric film, and the dielectric constant of the dielectric component is obtained from each parameter. Using the dielectric constant of the component and the dielectric constant of the air component, it is obtained by an arithmetic expression related to the effective medium approximation.

Next, an example of analysis performed on a sample on which a ferroelectric film is formed using the above-described sample analysis method of the present invention will be described. First, a sample in which a PZT film was formed on a Si (silicon) substrate provided with a Pt (platinum) film on the surface by vapor deposition was used. PZT is a substance in which lead titanate (PbTiO ₃ ) and lead zirconate (PbZrO ₃ ) are mixed, and belongs to a ferroelectric.

  Further, in this analysis example, as a model S ′ corresponding to the sample with the structure shown in FIG. 2B, PZT (substance M) is 30% (mixing ratio is 0.3) based on the effective medium approximation. A model S ′ in which a film S2 ′ having a void V of 70% (mixing ratio is 0.7) is formed on the Pt film S1 ′ of the Si substrate is created, and the film thickness d ′ of the film S2 ′ is set to 900 angstroms. Set to. In creating the model, a known reference is used for the Pt film on the substrate, and for the complex permittivity ε of the PZT film, Equation (7), which is an arithmetic expression related to the following effective medium approximation, and the above-described formula The dispersion formula of Formula (4) was used. For the air gap, a numerical value (about 1.003) equivalent to that of air was used for the refractive index.

In Equation (7), ε is the effective complex dielectric constant of the PZT film (film S2 ′), ε _a is the dielectric constant of PZT (substance M: PZT component) in the PZT film, and ε _b is in the PZT film. Is the dielectric constant of the void (air component) V, f _a is the mixing ratio of PZT, f _b is the mixing ratio of the void, and the overall effective complex dielectric constant of the PZT film was obtained based on Equation (7). .

The graph of FIG. 6A shows the measured value of the above-described sample by the ellipsometer 1 and the calculated value theoretically calculated from the model created first. As shown in the graph of FIG. 6A, when the measured value and the calculated value are compared, there is a clear difference between the measured value and the calculated value related to the phase difference Δ and the amplitude ratio Ψ. From such a state, the film thickness d ′ of the film S2 ′, the mixing ratio of the voids, the mixing ratio of PZT, and the parameters of the dispersion formula of Expression (4) were fitted. In the case of this analysis example, only ε _s , ω _t , and Γ ₀ were fitted to the dispersion formula among the parameters of the formula (4).

FIG. 6B is a graph after fitting, and FIG. 7 is a chart showing the results of fitting. As shown in the graph of FIG. 6 (b), the calculated value calculated from the model after the fitting is in a state substantially in agreement with the measured value of the ellipsometer 1 even in the range of about 250 nm to 400 nm. The value of the mean square error χ ² was about 6.57, which was a sufficiently small value. In this state, the ratio of PZT to the film S2 ′ is about 28.7%, which indicates that there are about 71.3% of voids. Further, the dielectric constant (ε _s ) at a low frequency of the PZT component of the film S2 ′ was about 372.79.

  FIG. 8 is a graph showing the refractive index n and extinction coefficient k of the PZT film calculated from the values specified by the fitting described above. As described above, by using the sample analysis method of the present invention, analysis can be performed even in the range of 400 nm or less, which has been impossible in the past, and stable analysis can be realized in the range of 248 nm to 826 nm. The horizontal axis of the graph of FIG. 8 uses photon energy that can be converted from the wavelength as a unit (5 eV = about 248 nm).

In addition, since the sample analysis method of the present invention can analyze a sample in which a dielectric film having a dielectric constant of 50 or more based on electrical measurement is formed on a substrate, in addition to the sample having the PZT film described above. A sample having a SrBi ₄ Ti ₄ O ₁₅ film can also be suitably analyzed. For a sample having a plurality of dielectric films (dielectric constant based on electrical measurement is 50 or more), it is shown in FIG. By applying such a model structure to each dielectric film layer and performing the same calculation as described above, analysis can be performed without any problem. Furthermore, the equation (4) related to the dispersion equation and the equation (7) related to the effective medium approximation are merely examples, and a well-known equation suitable for the sample to be analyzed may be appropriately used.

  In the sample analysis method of the present invention, it is also possible to analyze a sample by fitting each parameter for each of a plurality of stages, in addition to fitting all parameters at once as described above. Fitting all the parameters at once is suitable when the dispersion formula of the sample is known, or when the difference between the calculated value from the model created first and the measured value of the ellipsometer is small. The fitting at each stage is suitable when the dispersion formula of the sample is not known or when the difference between the calculated value from the created model and the measured value of the ellipsometer is large.

  In the present invention, as an example when performing fitting at each stage, first, four types of models with voids of 60%, 70%, 80%, and 90% are set for the film in which voids are formed. The calculated value and the measurement result of the ellipsometer 1 are compared, and a model (void) whose difference is reduced by the least square method is specified. Next, systematic analysis is performed on the identified void by fitting the parameters of the film thickness and the dispersion formula. Furthermore, after specifying the voids in this way, a model (film thickness) in which differences are similarly set by setting a plurality of types of film thicknesses is specified, and the parameters of the dispersion formula are specified for the specified voids and film thicknesses. It is also possible to perform analysis by fitting only.

It is the schematic which shows the structure of the ellipsometer and computer which are used for the sample analysis method of this invention. (A) is sectional drawing of a sample, (b) is the schematic which shows the structure of the model which has the space | gap based on effective medium approximation. It is the schematic which shows the internal structure of a spectrometer. It is the schematic which shows the setting menus, such as a film thickness and a void. It is a flowchart which shows the process which concerns on the sample analysis method of this invention. (A) is a graph which shows the calculated value from the model created initially, and the measured value by an ellipsometer, (b) is a graph which shows the calculated value and measured value after fitting. It is a graph which shows the result which concerns on fitting. It is a graph which shows a refractive index and an extinction coefficient. It is a graph which shows the measurement result of the ellipsometer with respect to a silicon oxide. (A) is a schematic diagram showing the structure of a sample, (b) is a schematic diagram of a sample having roughness on the film surface, and (c) is a schematic diagram showing the structure of a model having voids based on the effective medium approximation. FIG.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Ellipsometer 3 Light irradiation device 4 Stage 5 Light acquisition device 7 Spectrometer 8 Data acquisition device 10 Computer S Sample S 'Model S1 Substrate S2, S2' Film M Material V Void

Claims (2)

In an ellipsometer, the step of injecting light in a polarized state onto a sample in which a dielectric film having a dielectric constant of 50 or more based on electrical measurement is formed on a substrate;
Measuring a change in polarization state of incident light and reflected light on the sample;
Setting a condition according to the sample, and creating a model in which the void based on the effective medium approximation exists in the range of 60% to 90%;
Calculating a value corresponding to a change value of the polarization state measured by the ellipsometer based on the created model;
Comparing the calculated value with the change value measured with the ellipsometer;
A step of performing an operation using an arithmetic expression related to the effective medium approximation and a dispersion expression related to the model so that a difference between the two values compared becomes small;
And a step of analyzing the sample based on the result of the calculation. The dispersion formula includes a parameter related to a dielectric constant with respect to an optical measurement range,
The sample analysis method according to claim 1, wherein a dielectric constant is analyzed with respect to an optical measurement range of the dielectric film of the sample based on a numerical value of a parameter relating to the dielectric constant.

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